Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators Articles uri icon

publication date

  • December 2020

start page

  • 063112-1

end page

  • 063112-7

issue

  • 6

volume

  • 102

International Standard Serial Number (ISSN)

  • 2469-9926

Electronic International Standard Serial Number (EISSN)

  • 2469-9934

abstract

  • Two-dimensional (2D) systems with time-dependent controls admit a quadratic Hamiltonian modeling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some systems are not separable into independent modes by a point transformation. For these "coupled systems" 2D invariants may still guide the Hamiltonian design. The theory to perform the inversion and two application examples are provided: (i) We control the deflection of wave packets in transversally harmonic wave guides and (ii) we design the state transfer from one coupled oscillator to another.